I think "стане" and "се случи" both mean "to happen", while "стори" is a synonym of "чини" and "направи" meaning "to do/make". But there may be some peculiarities in Macedonian with which I'm not familiar.

Yes, and as you mentioned, "стане" is more casual, while "случи" is more formal. Both can be used in either spoken or written language:

Нищо не е станало = Нищо не се е случило = Nothing happened

Стори/Струва on the other hand has three meanings:
1. "To cost" for example: Колко струва? = How much does it cost?
2. "To seem": Стори ми се, че... = It seemed to me, that...
3. "To do": Какво да сторя? = What should I do? (This is now archaic)

"Стане" is not used in Macedonian as a synonym for "се случи" as often as in Bulgarian. "Стане" is more like "to become + noun" or "to get + adverb": get rich = стани богат, become a doctor = стани доктор). While "стори" is "to do/to make" as Vulcho already said, "се случи" is straight forward "to happen".